A seal system of this type, which may also be referred to as an intermediate stage seal, is known, for example, from EP 2 696 039 A1, also published as U.S. Patent Application Publication 2014/0044537 A1. In the seal system disclosed therein, the first flange section is pressed against the sealing section of the inner shroud section during operation, due to the pressure ratios in the turbine, so that a secondary sealing point is formed. However, hot working medium may nevertheless flow through the secondary sealing point, due to the pressure ratios (pressure difference over the guide blade system) and existing manufacturing tolerances. During startup of the turbomachine, in particular the two radially outwardly extending flange sections of the seal carrier, and thus the seal carrier itself, may be heated up thereby, whereby the latter's diameter is increased. A distance between the radially inner sealing element and the rotor-side sealing projections, which together form a primary sealing point, is enlarged hereby, so that the sealing action thereof deteriorates. The rotor-side sealing projections may also be referred to as sealing tips.